MathLiveIntegration by substitution
Converts a definite integral of a composite function into an integral over a new variable by substituting t = φ(x). It is used to simplify integrals whose integrand contains a function and its derivative.
\int_a^b f(\phi(x)) \phi'(x) \, \mathrm{d}x = \int_{\phi(a)}^{\phi(b)} f(t) \, \mathrm{d}tWhat the symbols mean
| a continuous function being integrated | |
| a continuously differentiable substitution function of x | |
| the derivative of \phi with respect to x | |
| lower limit of integration in x | |
| upper limit of integration in x | |
| the new integration variable, t = \phi(x) |
About this formula
- FieldMathematics
- TopicIntegration techniques
- LevelUniversity
- Also calledu-substitution, reverse chain rule, change of variables, substitution rule for definite integrals, u-substitution formula, change of variables in integral
- SourceWikidata Q1071270
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